A sonar transducer has a head mass at a distal end thereof, a tail mass at a proximal end thereof, a driver in physical contact with the head mass and the tail mass, and a flextensional body incorporating and extending proximally from the head mass. The flextensional body has relatively thin walls or diaphragms with concave surfaces. The sonar transducer may have a fundamental mode having a relatively low resonant frequency, involving substantially only a bending motion of the diaphragms. A second resonant mode, at a frequency higher than the frequency associated with the fundamental mode, involves both a bending motion of the diaphragms and a membrane or breathing motion of the flextensional body, including the head mass. A third, relatively high frequency resonant mode, involves exclusively or substantially exclusively longitudinal motion of the head mass.